In the field of antenna array systems it is well known to use antenna elements in the antenna array to shape a beam sent out from the antenna array. It is also known to let all the antenna elements in the antenna array receive signals. When the antenna array receives the signals it is possible to use one or several of the antenna elements, or even sub-array systems comprising a number of antenna elements. The antenna array can be used, for example, in a radar system or a sonar system and is intended to be used in trying to estimate the direction-of-arrival of a target.
When using the antenna array applications there is a wish to obtain high resolution and accurate estimation of the direction-of-arrival of the target. In order to gain the best performance possible it is common knowledge that there has to be a trade off between the standard deviation σ (or variance σ2) of the angle for detecting the target and the SNR (Signal to Noice Ratio). The higher the SNR the lower the standard deviation. The standard deviation is coupled to the probability of finding the target. The higher the standard deviation the lower the probability. The so-called “Cramér-Rao Lower Boundary (CRB)”, defines the theoretically best ratio between the SNR and the standard deviation σ for Additive White Gaussian noise (AWGN) signals. It is the desire of every antenna user to have a system that performs as close as possible to the CRB. This is due to the fact that for a given SNR the lower the standard deviation the closer to the CRB, i.e. the better the accuracy of direction-of-arrival estimation of a target.
However, the SNR is also coupled to the performance of the antenna system and the size of the targets. The performance refers to the probability of estimating the direction of arrival of a target. The accuracy depends on the width of the top of the main lobe, if the target is represented by the main lobe. The higher the SNR the more narrow the top of the main lobe. It is the tapering of the main lobe and the pointyness of the main lobe that tells where the maximum of the main lobe can be found in a radiation diagram. The more pointed the lobe the better the measuring accuracy when finding the main lobe maximum, i.e. the better measuring accuracy when estimating the direction of arrival of a target.
The lower limit for the SNR, i.e. the lowest performance possible for the antenna system, occurs where the noise in the signal drowns the signal from the target. This becomes clear if one follows the CRB when diminishing the SNR. The standard deviation increases with decreasing SNR i.e. it becomes more difficult to correctly estimate the direction of arrival of the target the lower the SNR. A strong signal compared to a low noise gives a high SNR and a low uncertainty of the estimation of the direction-of-arrival of the target, and vice versa for a low SNR.
It is a desirable feature for an antenna system to have the ability to detect and estimate the direction of arrival of the target with a reasonable probability (reasonably low standard deviation). An optimum is thus sought for the trade off between low standard deviation and low SNR.
As has been stated above, one way to obtain an antenna system with good direction finding ability is to narrow the main lobe. This can be carried out by separating the antenna elements in the antenna array. The more separated the elements are the more narrow the main lobe becomes and thus the better direction finding ability of the system.
However, the separation of the antenna elements give rise to grating lobes due to the so-called Spatial Aliasing Phenomena. The problem with grating lobes occurs when the antenna elements are separated by more than half a wavelength λ, i.e. at the Nyqvist frequency. The grating lobes are mathematical products that will appear in an antenna diagram showing a radiation diagram of the gain G (θ) versus the azimuth angle θ. The integral over the radiation diagram is constant independent on the size of the main lobe and the size and number of the grating lobes, i.e. the more grating lobes the lesser and narrower the main lobe.
The grating lobes will appear on each side of the main lobe and with decreased amplitude the further away from the main lobe they are found. The two grating lobes closest to the main lobe have the highest amplitude. The grating lobes are thus dependent of the angle and can be interpreted as signals from the main lobe seen from the side angle θ.
The grating lobes cause problems when trying to detect the direction of arrival of a target. The target will randomly skip between the grating lobes for low SNR and will therefore create random errors regarding the detection probability of the target. Thus, the grating lobes generate a high standard deviation.
As has been described above, the more separated the antennas are, the larger the antenna becomes and the narrower the main lobe. The narrower the main lobe the better the direction detection probability, i.e. the better the estimation of direction-of-arrival. However, the more separated the antennas are, the more and the higher the grating lobes will appear in the radiation diagram of the antenna array.
To sum up the above, when the antenna elements are separated far enough to give a narrow enough main lobe to get a good estimation of direction-of-arrival, the grating lobes will cause an uncertainty because the target skips between the main lobe and the grating lobes.
It is an object of the technology to diminish random errors regarding the resolving probability of the target when trying to narrow the main lobe, in order to get better estimation of the direction-of-arrival of a target. It is thus an object of the technology to eliminate the grating lobe problem when trying to “zoom in” on a target, i.e. to achieve a better measuring accuracy.